[petsc-users] Null space of discrete Laplace with periodic boundary conditions

Jed Brown jedbrown at mcs.anl.gov
Tue Feb 14 09:25:58 CST 2012

On Tue, Feb 14, 2012 at 09:20, Thomas Witkowski <
thomas.witkowski at tu-dresden.de> wrote:

> I discretize the Laplace operator (using finite element) on the unit
> square equipped with periodic boundary conditions on all four edges. Is it
> correct that the null space is still constant? I wounder, because when I
> run the same code on a sphere (so a 2D surface embedded in 3D), the
> resulting matrix is non-singular. I thought, that both cases should be
> somehow equal with respect to the null space?

The continuum operators for both cases have a constant null space, so if
either is nonsingular in your finite element code, it's a discretization
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